We study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor associated with the conformal Killing field. With these assumptions we find an explicit relationship relating two metric components of the metric tensor field. This leads to the general solution of the Einstein field equations with a conformal symmetry in a static spherically symmetric spacetime. For perfect fluids we can find all metrics explicitly and show that the models always admit a barotropic equation of state. Contained within this class of spacetimes are the well known metrics of (interior) Schwarzschild, Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. The isothermal metric of Saslaw et al also admits a conformal symmetry. For imperfect fluids an infinite family of exact solutions to the field equations can be generated.
We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints.
We investigate the role played by conformal symmetries in the study of exact solutions in static spherically symmetric spacetimes. We consider the gravitational field associated with anisotropic charged fluids. The existence of a conformal symmetry provides us with a functional relation between the metric functions. This relationship yields a general solution to the Einstein-Maxwell equations. Various conformally symmetric models for fluids that are charged or anisotropic or both are shown to be special cases of the general exact solution generated in this paper. In particular we generate a conformally flat Finch-Skea type model for an isotropic charged fluid.
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